Answer:
Therefore, the surface area of the composite figure is 368 cm².
Explanation:
To find the surface area of the composite figure, we need to find the areas of each individual face and add them together.
The triangular prism has two triangular faces and three rectangular faces.
The area of each triangular face is 1/2(base × height).
Area of each triangular face = 1/2(10 × 5) = 25 cm²
The area of each rectangular face is length × width.
Area of the rectangular face with dimensions 5 cm by 10 cm = 5 × 10 = 50 cm²
Area of the rectangular face with dimensions 5 cm by 10 cm = 5 × 10 = 50 cm²
Area of the rectangular face with dimensions 10 cm by 8 cm = 10 × 8 = 80 cm²
Total area of the triangular prism = 2 × 25 + 3 × 50 + 80 = 280 cm²
The rectangular prism has two rectangular faces and four square faces.
The area of each rectangular face is length × width.
Area of the rectangular face with dimensions 4 cm by 5 cm = 4 × 5 = 20 cm²
Area of the rectangular face with dimensions 4 cm by 5 cm = 4 × 5 = 20 cm²
The area of each square face is side × side.
Area of each square face with side length 4 cm = 4 × 4 = 16 cm²
Total area of the rectangular prism = 2 × 20 + 4 × 16 = 88 cm²
The total surface area of the composite figure is the sum of the surface areas of the triangular prism and the rectangular prism.
Total surface area = surface area of triangular prism + surface area of rectangular prism
= 280 cm² + 88 cm²
= 368 cm²